Question:
Convert \(12.125\) decimal into binary
Convert \(12.125\) decimal into binary
Show Hint
To convert a decimal fraction into binary,
\[
\boxed{
\text{Repeatedly multiply the fractional part by }2.
}
\]
The integer parts obtained form the binary fraction.
Updated On: Jul 14, 2026
- \(1100.111\)
- \(1100.001\)
- \(1100.110\)
- \(1100.101\)
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The Correct Option is B
Solution and Explanation
Step 1: Convert the integer part.
The integer part is
\[
12_{10}=1100_2.
\]
Step 2: Convert the fractional part. The fractional part is \[ 0.125. \] Multiply successively by \(2\): \[ 0.125\times2=0.25\quad\Rightarrow\quad0 \] \[ 0.25\times2=0.5\quad\Rightarrow\quad0 \] \[ 0.5\times2=1.0\quad\Rightarrow\quad1 \] Hence, \[ 0.125_{10}=0.001_2. \] Therefore, \[ 12.125_{10}=1100.001_2. \] Thus, \[ \boxed{1100.001} \] Therefore, \[ \boxed{(B)} \] is the correct answer.
Step 2: Convert the fractional part. The fractional part is \[ 0.125. \] Multiply successively by \(2\): \[ 0.125\times2=0.25\quad\Rightarrow\quad0 \] \[ 0.25\times2=0.5\quad\Rightarrow\quad0 \] \[ 0.5\times2=1.0\quad\Rightarrow\quad1 \] Hence, \[ 0.125_{10}=0.001_2. \] Therefore, \[ 12.125_{10}=1100.001_2. \] Thus, \[ \boxed{1100.001} \] Therefore, \[ \boxed{(B)} \] is the correct answer.
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